package edu.princeton.cs.algs4;

/*************************************************************************
 *  Compilation:  javac ClosestPair.java
 *  Execution:    java ClosestPair < input.txt
 *  Dependencies: Point.java
 *  
 *  Given N points in the plane, find the closest pair in N log N time.
 *
 *  Note: could speed it up by comparing square of Euclidean distances
 *  instead of Euclidean distances.
 *
 *************************************************************************/

import java.util.Arrays;

import edu.princeton.cs.stdlib.StdIn;

public class ClosestPair {

	// closest pair of points and their Euclidean distance
	private Point best1, best2;
	private double bestDistance = Double.POSITIVE_INFINITY;

	public ClosestPair(Point[] points) {
		int N = points.length;
		if (N <= 1)
			return;

		// sort by x-coordinate (breaking ties by y-coordinate)
		Point[] pointsByX = new Point[N];
		for (int i = 0; i < N; i++)
			pointsByX[i] = points[i];
		Arrays.sort(pointsByX, Point.BY_X);

		// check for coincident points
		for (int i = 0; i < N - 1; i++) {
			if (pointsByX[i].equals(pointsByX[i + 1])) {
				bestDistance = 0.0;
				best1 = pointsByX[i];
				best2 = pointsByX[i + 1];
				return;
			}
		}

		// sort by y-coordinate (but not yet sorted)
		Point[] pointsByY = new Point[N];
		for (int i = 0; i < N; i++)
			pointsByY[i] = pointsByX[i];

		// auxiliary array
		Point[] aux = new Point[N];

		closest(pointsByX, pointsByY, aux, 0, N - 1);
	}

	// find closest pair of points in pointsByX[lo..hi]
	// precondition: pointsByX[lo..hi] and pointsByY[lo..hi] are the same
	// sequence of points
	// precondition: pointsByX[lo..hi] sorted by x-coordinate
	// postcondition: pointsByY[lo..hi] sorted by y-coordinate
	private double closest(Point[] pointsByX, Point[] pointsByY, Point[] aux,
			int lo, int hi) {
		if (hi <= lo)
			return Double.POSITIVE_INFINITY;

		int mid = lo + (hi - lo) / 2;
		Point median = pointsByX[mid];

		// compute closest pair with both endpoints in left subarray or both in
		// right subarray
		double delta1 = closest(pointsByX, pointsByY, aux, lo, mid);
		double delta2 = closest(pointsByX, pointsByY, aux, mid + 1, hi);
		double delta = Math.min(delta1, delta2);

		// merge back so that pointsByY[lo..hi] are sorted by y-coordinate
		Merge.merge(pointsByY, aux, lo, mid, hi);

		// aux[0..M-1] = sequence of points closer than delta, sorted by
		// y-coordinate
		int M = 0;
		for (int i = lo; i <= hi; i++) {
			if (Math.abs(pointsByY[i].x() - median.x()) < delta)
				aux[M++] = pointsByY[i];
		}

		// compare each point to its neighbors with y-coordinate closer than
		// delta
		for (int i = 0; i < M; i++) {
			// a geometric packing argument shows that this loop iterates at
			// most 7 times
			for (int j = i + 1; (j < M) && (aux[j].y() - aux[i].y() < delta); j++) {
				double distance = aux[i].distanceTo(aux[j]);
				if (distance < delta) {
					delta = distance;
					if (distance < bestDistance) {
						bestDistance = delta;
						best1 = aux[i];
						best2 = aux[j];
						// StdOut.println("better distance = " + delta +
						// " from " + best1 + " to " + best2);
					}
				}
			}
		}
		return delta;
	}

	public Point either() {
		return best1;
	}

	public Point other() {
		return best2;
	}

	public double distance() {
		return bestDistance;
	}

	public static void main(String[] args) {
		int N = StdIn.readInt();
		Point[] points = new Point[N];
		for (int i = 0; i < N; i++) {
			int x = StdIn.readInt();
			int y = StdIn.readInt();
			points[i] = new Point(x, y);
		}
		ClosestPair closest = new ClosestPair(points);
		System.out.println(closest.distance() + " from " + closest.either()
				+ " to " + closest.other());
	}

}
